Volume Of Solid Of Revolution Given Lateral Surface Area Calculator

Formula Used:

\[ V = (2\pi A_{Curve}) \times \left( \frac{LSA + \pi (r_{Top} + r_{Bottom})^2}{2\pi A_{Curve} R_{A/V}} \right) \]

Area under Curve Solid of Revolution:

m²

Lateral Surface Area of Solid of Revolution:

m²

Top Radius of Solid of Revolution:

Bottom Radius of Solid of Revolution:

Surface to Volume Ratio of Solid of Revolution:

1/m

Volume of Solid of Revolution:

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1. What is Volume of Solid of Revolution?

The Volume of Solid of Revolution is the total quantity of three dimensional space enclosed by the entire surface of the Solid of Revolution formed by rotating a curve around a fixed axis.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = (2\pi A_{Curve}) \times \left( \frac{LSA + \pi (r_{Top} + r_{Bottom})^2}{2\pi A_{Curve} R_{A/V}} \right) \]

Where:

\( V \) — Volume of Solid of Revolution (m³)
\( A_{Curve} \) — Area under Curve Solid of Revolution (m²)
\( LSA \) — Lateral Surface Area of Solid of Revolution (m²)
\( r_{Top} \) — Top Radius of Solid of Revolution (m)
\( r_{Bottom} \) — Bottom Radius of Solid of Revolution (m)
\( R_{A/V} \) — Surface to Volume Ratio of Solid of Revolution (1/m)
\( \pi \) — Archimedes' constant (≈3.1416)

Explanation: This formula calculates the volume of a solid formed by rotating a curve around an axis, considering the area under the curve, lateral surface area, top and bottom radii, and surface to volume ratio.

3. Importance of Volume Calculation

Details: Accurate volume calculation is crucial for determining the capacity of revolution solids, which has applications in engineering, manufacturing, architecture, and various scientific fields.

4. Using the Calculator

Tips: Enter all required values in appropriate units. Ensure all values are positive numbers. The calculator will compute the volume based on the provided inputs.

5. Frequently Asked Questions (FAQ)

Q1: What types of solids can this calculator handle?
A: This calculator can handle various solids of revolution including those formed by rotating curves around horizontal or vertical axes.

Q2: What are typical units for these measurements?
A: Area is typically in square meters (m²), length measurements in meters (m), volume in cubic meters (m³), and surface to volume ratio in per meter (1/m).

Q3: Can this calculator handle negative values?
A: No, all input values must be positive numbers as they represent physical quantities that cannot be negative.

Q4: How accurate are the results?
A: The results are mathematically precise based on the input values and the formula. The accuracy depends on the precision of the input measurements.

Q5: What if I get an error or unexpected result?
A: Double-check that all input values are positive numbers and that you've entered them in the correct units. Ensure all required fields are filled.